Subgroups — #25119166

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583016	C₂	1	1	yes	maximal, characteristic, complemented
2	#19143322	C₂	1	2	yes	maximal, complemented
3	C₂×#14582948	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135489	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135344	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135245	C₂	1	2	yes	maximal, complemented
7	#19134898	C₂	1	2	yes	maximal, complemented
8	#19134872	C₂	1	2	yes	maximal, complemented
9	#19134481	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134376	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	C₂²	1	2	yes	—
13	C₂²×#10621877	C₂²	1	2	yes	—
14	#14583016	—	2	4	no	—
15	#14582977	—	2	2	no	—
16	#14582971	—	2	2	no	—
17	#14582971	—	2	2	no	—
18	D₄×C₄₃⋊C₈	—	2	2	no	—
19	#14582948	—	2	4	no	—
20	C₂×#13063261	C₂²	1	1	yes	characteristic
21	C₂×#13063261	C₂²	1	2	yes	—
22	C₂×#13063261	C₂²	1	1	yes	characteristic
23	#14582926	C₂²	1	2	yes	—
24	C₂×#13063252	C₂²	1	2	yes	—
25	C₂×#13063252	C₂²	1	2	yes	—
26	#14582866	C₂²	1	2	yes	—
27	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	#14582855	C₂²	1	2	yes	—
29	C₂×#13063235	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	#14582658	C₂²	1	2	yes	—
33	#14582658	C₂²	1	2	yes	—
34	#14582653	C₂²	1	1	yes	characteristic
35	#14582653	C₂²	1	1	yes	characteristic
36	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#525	C₂²	1	2	yes	—
39	C₄₃×#470	C₄	1	2	yes	complemented
40	C₄₃×#469	C₄	1	2	yes	complemented
41	C₄₃×#468	C₄	1	2	yes	complemented
42	C₄₃×#468	C₄	1	2	yes	complemented
43	C₄₃×#427	C₂²	1	1	yes	characteristic
44	C₄₃×#416	C₂²	1	2	yes	—
45	#13063332	—	2	4	no	—
46	#13063332	—	4	2	no	—
47	C₂×#10621877	—	2	2	no	—
48	C₂×#10621877	—	2	2	no	—
49	C₂×#10621877	—	2	4	no	—
50	C₂×#10621877	—	4	2	no	—
51	C₂×#10621877	C₂³	1	2	yes	—
52	C₂×#10621877	C₂³	1	2	yes	—
53	C₂²×C₄₃⋊C₈	—	2	2	no	—
54	C₂²×C₄₃⋊C₈	—	2	2	no	—
55	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
58	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
60	#13063261	—	2	2	no	—
61	#13063261	—	2	4	no	—
62	#13063261	D₄	1	4	yes	complemented
63	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
65	#13063252	—	2	4	no	—
66	#13063252	—	4	2	no	—
67	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
68	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
69	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
70	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
71	#13063236	—	2	2	no	—
72	#13063235	—	2	2	no	—
73	C₄×C₄₃⋊C₈	—	2	2	no	—
74	C₈×Dic₄₃	—	2	2	no	—
75	C₄₃⋊#95	—	2	1	no	—
76	C₂×#41×C₄₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	#135×C₄₃	—	2	2	no	—
79	#135×C₄₃	—	2	2	no	—
80	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×M₁₆×C₄₃	—	2	2	no	—
84	C₂×M₁₆×C₄₃	—	2	2	no	—
85	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	#123×C₄₃	—	2	2	no	—
90	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
91	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
92	#121×C₄₃	C₂×C₄	1	2	yes	—
93	#121×C₄₃	C₂×C₄	1	2	yes	—
94	#120×C₄₃	—	2	2	no	—
95	C₄×D₄×C₄₃	—	2	2	no	—
96	C₄×D₄×C₄₃	—	2	2	no	—
97	#117×C₄₃	C₂³	1	2	yes	—
98	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
99	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
100	#106×C₄₃	C₂×C₄	1	2	yes	—
101	#103×C₄₃	C₂×C₄	1	2	yes	—
102	#103×C₄₃	C₂×C₄	1	2	yes	—
103	#102×C₄₃	C₂×C₄	1	2	yes	—
104	#102×C₄₃	C₂×C₄	1	2	yes	—
105	C₂⁴×C₄₃	#41	1	1	yes	characteristic
106	#41×C₄₃	—	2	2	no	—
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²×Dic₄₃	—	2	1	no	—
125	C₂²×Dic₄₃	—	2	1	no	—
126	Q₁₆×C₄₃	—	2	2	no	—
127	SD₁₆×C₄₃	—	2	4	no	—
128	D₈×C₄₃	—	2	2	no	—
129	M₁₆×C₄₃	—	2	4	no	—
130	M₁₆×C₄₃	—	2	4	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₄₃	#41	1	2	yes	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₄₃	—	2	2	no	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂²⋊C₄×C₄₃	—	2	2	no	—
146	C₂²⋊C₄×C₄₃	—	2	2	no	—
147	C₄²×C₄₃	—	2	2	no	—
148	C₂²⋊Dic₄₃	—	4	2	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₄×Dic₄₃	—	2	1	no	—
152	C₄×Dic₄₃	—	2	1	no	—
153	#10621877	—	2	2	no	—
154	#10621877	—	2	2	no	—
155	#10621877	—	2	2	no	—
156	#10621877	—	4	4	no	—
157	#10621877	—	4	4	no	—
158	#10621877	C₂×D₄	1	4	yes	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	2	1	no	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	—	2	1	no	—
164	C₂×C₄₃⋊C₈	—	2	2	no	—
165	C₂×C₄₃⋊C₈	—	4	4	no	—
166	C₂×C₄₃⋊C₈	—	4	4	no	—
167	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
168	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂³×C₄₃	—	2	1	no	—
171	C₂³×C₄₃	—	2	1	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	4	1	no	—
174	C₂³×C₄₃	—	4	1	no	—
175	C₂³×C₄₃	C₄×D₄	1	2	yes	—
176	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
177	Q₈×C₄₃	—	2	2	no	—
178	Q₈×C₄₃	—	2	2	no	—
179	D₄×C₄₃	—	2	2	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	4	4	no	—
182	D₄×C₄₃	—	4	2	no	—
183	D₄×C₄₃	—	4	2	no	—
184	D₄×C₄₃	—	8	2	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×Dic₄₃	—	2	2	no	—
204	C₂×Dic₄₃	—	4	1	no	—
205	C₂×Dic₄₃	—	4	1	no	—
206	C₂×Dic₄₃	—	4	1	no	—
207	C₂×Dic₄₃	—	4	1	no	—
208	C₂×Dic₄₃	—	4	1	no	—
209	C₈×C₄₃	—	2	2	no	—
210	C₈×C₄₃	C₄×D₄	1	2	yes	—
211	C₈×C₄₃	C₄×D₄	1	2	yes	—
212	C₄₃⋊C₈	—	2	1	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	2	4	no	—
215	C₄₃⋊C₈	—	2	2	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	#23020	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	—	2	1	no	—
219	C₂²×C₄₃	—	2	1	no	—
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	2	2	no	—
222	C₂²×C₄₃	—	2	2	no	—
223	C₂²×C₄₃	—	4	2	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	—	8	1	no	—
227	C₂²×C₄₃	—	8	1	no	—
228	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₄₃	#548	1	1	yes	characteristic
230	C₂²×C₄₃	#553	1	1	yes	characteristic
231	C₄×C₄₃	—	2	2	no	—
232	C₄×C₄₃	—	4	2	no	—
233	C₄×C₄₃	—	4	2	no	—
234	C₄×C₄₃	—	4	2	no	—
235	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₄₃	#520	1	1	yes	characteristic
237	C₄×C₄₃	D₄²	1	1	yes	characteristic
238	C₄×C₄₃	#547	1	1	yes	characteristic
239	Dic₄₃	—	4	2	no	—
240	Dic₄₃	—	8	1	no	—
241	#3054	D₄₃	1	1	yes	characteristic
242	C₂×#443	—	43	1	no	—
243	#2933	—	43	2	no	—
244	C₂×#430	—	43	1	no	—
245	#1975	—	43	1	no	—
246	#1945	—	43	1	no	—
247	#1929	—	43	2	no	—
248	#1871	—	43	2	no	—
249	#1866	—	43	2	no	—
250	#1773	—	43	1	no	—
251	#1753	—	43	1	no	—
252	C₂×C₄₃	—	2	1	no	—
253	C₂×C₄₃	—	2	1	no	—
254	C₂×C₄₃	—	4	2	no	—
255	C₂×C₄₃	—	8	2	no	—
256	C₂×C₄₃	#2361	1	1	yes	characteristic
257	C₂×C₄₃	#2955	1	1	yes	characteristic
258	C₂×C₄₃	#2956	1	1	yes	characteristic
259	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
260	C₂×#131	—	43	2	no	—
261	C₂²×M₁₆	—	43	2	no	—
262	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
263	#525	C₂×D₄₃	1	2	yes	—
264	#470	Dic₄₃	1	2	yes	complemented
265	#469	Dic₄₃	1	2	yes	complemented
266	#468	Dic₄₃	1	2	yes	complemented
267	#468	Dic₄₃	1	2	yes	complemented
268	#443	—	86	4	no	—
269	#436	—	86	2	no	—
270	#435	—	86	2	no	—
271	#435	—	86	2	no	—
272	C₈×D₄	—	86	2	no	—
273	#430	—	86	4	no	—
274	C₂×#108	—	43	1	no	—
275	C₂×#108	—	43	2	no	—
276	C₂×#108	—	43	1	no	—
277	#427	C₂×D₄₃	1	1	yes	characteristic
278	#424	—	43	2	no	—
279	C₂×#104	—	43	2	no	—
280	C₂×#104	—	43	2	no	—
281	#416	C₂×D₄₃	1	2	yes	—
282	#408	—	43	2	no	—
283	C₂×C₂²⋊C₈	—	43	1	no	—
284	#405	—	43	2	no	—
285	C₂×#97	—	43	1	no	—
286	C₂×C₄×C₈	—	43	1	no	—
287	C₄×C₂²⋊C₄	—	43	1	no	—
288	#339	—	43	2	no	—
289	#339	—	43	2	no	—
290	#336	—	43	1	no	—
291	#336	—	43	1	no	—
292	C₄₃	#23020	1	1	yes	characteristic, complemented, Sylow
293	C₂×#41	C₂²×D₄₃	1	2	yes	—
294	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	C₂×Q₁₆	C₂×Dic₄₃	1	1	yes	characteristic
298	C₂×SD₁₆	C₂×Dic₄₃	1	2	yes	—
299	C₂×D₈	C₂×Dic₄₃	1	1	yes	characteristic
300	#131	—	86	4	no	—
301	#131	—	172	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	43	2	no	—
305	C₂×M₁₆	—	43	2	no	—
306	C₂×M₁₆	—	86	2	no	—
307	C₂×M₁₆	—	86	2	no	—
308	C₂×M₁₆	—	86	4	no	—
309	C₂×M₁₆	—	172	2	no	—
310	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
311	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
312	C₂²×C₈	—	43	1	no	—
313	C₂²×C₈	—	43	1	no	—
314	C₂²×C₈	—	86	2	no	—
315	C₂²×C₈	—	86	2	no	—
316	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	#123	—	2	2	no	—
319	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
320	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
321	#121	C₂×Dic₄₃	1	2	yes	—
322	#121	C₂×Dic₄₃	1	2	yes	—
323	#120	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	#117	C₂²×D₄₃	1	2	yes	—
327	C₂×C₂²⋊C₄	—	86	1	no	—
328	C₂×C₄²	—	43	1	no	—
329	C₂×C₄²	—	43	1	no	—
330	#108	—	43	4	no	—
331	#108	—	86	4	no	—
332	#108	—	86	2	no	—
333	#107	C₂×Dic₄₃	1	1	yes	characteristic
334	#107	C₂×Dic₄₃	1	1	yes	characteristic
335	#106	C₂×Dic₄₃	1	2	yes	—
336	C₄⋊C₈	—	86	2	no	—
337	C₄⋊C₈	—	86	2	no	—
338	#104	—	86	4	no	—
339	#104	—	172	2	no	—
340	#103	C₂×Dic₄₃	1	2	yes	—
341	#103	C₂×Dic₄₃	1	2	yes	—
342	#102	C₂×Dic₄₃	1	2	yes	—
343	#102	C₂×Dic₄₃	1	2	yes	—
344	C₂²⋊C₈	—	43	2	no	—
345	C₂²⋊C₈	—	43	2	no	—
346	C₂²⋊C₈	—	86	2	no	—
347	C₂²⋊C₈	—	86	2	no	—
348	#97	—	86	2	no	—
349	#97	—	86	2	no	—
350	C₄×C₈	—	86	2	no	—
351	C₄×C₈	—	86	2	no	—
352	#95	—	86	1	no	—
353	C₂⁴	#10621900	1	1	yes	characteristic
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	—	86	1	no	—
370	C₂²×C₄	D₄×D₄₃	1	2	yes	—
371	C₂²×C₄	#10621900	1	1	yes	characteristic
372	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
373	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
374	Q₁₆	—	2	2	no	—
375	SD₁₆	—	2	4	no	—
376	D₈	—	2	2	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	43	4	no	—
380	M₁₆	—	86	2	no	—
381	M₁₆	—	86	2	no	—
382	M₁₆	—	86	2	no	—
383	M₁₆	—	172	4	no	—
384	M₁₆	—	172	4	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	43	2	no	—
388	C₂×C₈	—	43	1	no	—
389	C₂×C₈	—	43	1	no	—
390	C₂×C₈	—	86	1	no	—
391	C₂×C₈	—	86	2	no	—
392	C₂×C₈	—	86	1	no	—
393	C₂×C₈	—	86	1	no	—
394	C₂×C₈	—	86	1	no	—
395	C₂×C₈	—	86	2	no	—
396	C₂×C₈	—	172	4	no	—
397	C₂×C₈	—	172	4	no	—
398	C₂×C₈	D₄×D₄₃	1	2	yes	—
399	C₂×C₈	#10621900	1	2	yes	—
400	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
401	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
402	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
406	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	172	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	86	1	no	—
415	C₄²	—	86	1	no	—
416	C₄²	—	86	1	no	—
417	C₄²	—	86	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	D₄×Dic₄₃	1	2	yes	—
424	C₂³	C₂×#10621900	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	86	2	no	—
445	C₂×C₄	—	172	1	no	—
446	C₂×C₄	—	172	1	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	1	no	—
449	C₂×C₄	—	172	1	no	—
450	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
451	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
455	C₂×C₄	#13063371	1	1	yes	characteristic
456	C₂×C₄	#13063372	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	86	1	no	—
459	C₈	—	86	1	no	—
460	C₈	—	86	4	no	—
461	C₈	—	86	2	no	—
462	C₈	—	172	2	no	—
463	C₈	D₄×Dic₄₃	1	2	yes	—
464	C₈	D₄×Dic₄₃	1	2	yes	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
476	C₂²	#14583555	1	1	yes	characteristic
477	C₂²	#14583601	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	344	1	no	—
483	C₄	—	172	2	no	—
484	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
485	C₄	#14583382	1	1	yes	characteristic
486	C₄	#14583533	1	1	yes	characteristic
487	C₄	#14583549	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	2	no	—
492	C₂	#19137615	1	1	yes	characteristic
493	C₂	#19143498	1	1	yes	characteristic
494	C₂	#19143505	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting, prime radical	C₄₃×#3054	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#3054	D₄₃
hypocenter	C₄₃	#23020
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#14583016	C₂	semidirect
2. #19143322	C₂	semidirect
3. C₂×#14582948	C₂	semidirect
4. #19135489	C₂	semidirect
5. #19135344	C₂	semidirect
6. #19135245	C₂	semidirect
7. #19134898	C₂	semidirect
8. #19134872	C₂	semidirect
9. #19134481	C₂	semidirect
10. #19134376	C₂	semidirect
39. C₄₃×#470	C₄	semidirect
40. C₄₃×#469	C₄	semidirect
41. C₄₃×#468	C₄	semidirect
42. C₄₃×#468	C₄	semidirect
62. #13063261	D₄	semidirect
264. #470	Dic₄₃	semidirect
265. #469	Dic₄₃	semidirect
266. #468	Dic₄₃	semidirect
267. #468	Dic₄₃	semidirect
292. C₄₃	#23020	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14583016	2
#19143322	2
C₂×#14582948	2
#19135489	2
#19135344	2
#19135245	2
#19134898	2
#19134872	2
#19134481	2
#19134376	2
C₄₃×#3054	2
#23020	43